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Magazine Problem 139
Write the first five terms of the sequence. $$a_{n}=\frac{(-1)^{n} x^{n}}{n !}$$
Problem 140
Write the first five terms of the sequence. $$a_{n}=\frac{(-1)^{n} x^{n+1}}{(n+1) !}$$
Problem 143
Write the first five terms of the sequence. Then find an expression for the \(n\) th partial sum. $$a_{n}=\frac{1}{2 n}-\frac{1}{2 n+2}$$
Problem 144
Write the first five terms of the sequence. Then find an expression for the \(n\) th partial sum. $$a_{n}=\frac{1}{n}-\frac{1}{n+1}$$
Problem 145
Write the first five terms of the sequence. Then find an expression for the \(n\) th partial sum. $$a_{n}=\frac{1}{n+1}-\frac{1}{n+2}$$
Problem 146
Write the first five terms of the sequence. Then find an expression for the \(n\) th partial sum. $$a_{n}=\frac{1}{n}-\frac{1}{n+2}$$
Problem 147
Does every finite series whose terms are integers have a finite sum? Explain.
Problem 149
Find, if possible, (a) \(A-B,\) (b) \(2 B-3 A,\) (c) \(A B,\) and (d) \(B A.\) $$A=\left[\begin{array}{l}6 \\\3\end{array}\right], B=\left[\begin{array}{r}4 \\\\-3\end{array}\right]$$
Problem 150
Find, if possible, (a) \(A-B,\) (b) \(2 B-3 A,\) (c) \(A B,\) and (d) \(B A.\) $$A=\left[\begin{array}{cc}10 & 7 \\\\-4 & 6\end{array}\right], B=\left[\begin{array}{cc}0 & -12 \\\8 & 11\end{array}\right]$$
Problem 151
Find, if possible, (a) \(A-B,\) (b) \(2 B-3 A,\) (c) \(A B,\) and (d) \(B A.\) $$A=\left[\begin{array}{rrr}-2 & -3 & 6 \\\4 & 5 & 7 \\\1 & 7 & 4\end{array}\right], B=\left[\begin{array}{lll}1 & 4 & 2 \\\0 & 1 & 6 \\\0 & 3 & 1\end{array}\right]$$
